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Simplifying 0.325x2 + 0.0162x + -0.00646 = 0 Reorder the terms: -0.00646 + 0.0162x + 0.325x2 = 0 Solving -0.00646 + 0.0162x + 0.325x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.325 the coefficient of the squared term: Divide each side by '0.325'. -0.01987692308 + 0.04984615385x + x2 = 0 Move the constant term to the right: Add '0.01987692308' to each side of the equation. -0.01987692308 + 0.04984615385x + 0.01987692308 + x2 = 0 + 0.01987692308 Reorder the terms: -0.01987692308 + 0.01987692308 + 0.04984615385x + x2 = 0 + 0.01987692308 Combine like terms: -0.01987692308 + 0.01987692308 = 0.00000000000 0.00000000000 + 0.04984615385x + x2 = 0 + 0.01987692308 0.04984615385x + x2 = 0 + 0.01987692308 Combine like terms: 0 + 0.01987692308 = 0.01987692308 0.04984615385x + x2 = 0.01987692308 The x term is 0.04984615385x. Take half its coefficient (0.02492307693). Square it (0.0006211597637) and add it to both sides. Add '0.0006211597637' to each side of the equation. 0.04984615385x + 0.0006211597637 + x2 = 0.01987692308 + 0.0006211597637 Reorder the terms: 0.0006211597637 + 0.04984615385x + x2 = 0.01987692308 + 0.0006211597637 Combine like terms: 0.01987692308 + 0.0006211597637 = 0.0204980828437 0.0006211597637 + 0.04984615385x + x2 = 0.0204980828437 Factor a perfect square on the left side: (x + 0.02492307693)(x + 0.02492307693) = 0.0204980828437 Calculate the square root of the right side: 0.143171515 Break this problem into two subproblems by setting (x + 0.02492307693) equal to 0.143171515 and -0.143171515.Subproblem 1
x + 0.02492307693 = 0.143171515 Simplifying x + 0.02492307693 = 0.143171515 Reorder the terms: 0.02492307693 + x = 0.143171515 Solving 0.02492307693 + x = 0.143171515 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.02492307693' to each side of the equation. 0.02492307693 + -0.02492307693 + x = 0.143171515 + -0.02492307693 Combine like terms: 0.02492307693 + -0.02492307693 = 0.00000000000 0.00000000000 + x = 0.143171515 + -0.02492307693 x = 0.143171515 + -0.02492307693 Combine like terms: 0.143171515 + -0.02492307693 = 0.11824843807 x = 0.11824843807 Simplifying x = 0.11824843807Subproblem 2
x + 0.02492307693 = -0.143171515 Simplifying x + 0.02492307693 = -0.143171515 Reorder the terms: 0.02492307693 + x = -0.143171515 Solving 0.02492307693 + x = -0.143171515 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.02492307693' to each side of the equation. 0.02492307693 + -0.02492307693 + x = -0.143171515 + -0.02492307693 Combine like terms: 0.02492307693 + -0.02492307693 = 0.00000000000 0.00000000000 + x = -0.143171515 + -0.02492307693 x = -0.143171515 + -0.02492307693 Combine like terms: -0.143171515 + -0.02492307693 = -0.16809459193 x = -0.16809459193 Simplifying x = -0.16809459193Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.11824843807, -0.16809459193}
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